Find y' if arctan (xy) = 4 + xy².

The problem formed can be:

And the answer to the formed problem will be 26 miles.

So, using the above-given information about Angela, the problem that can be formed is:

To solve the problem, we will make a mathematical expression and then solve by mathematical operations as follows:

Therefore, the problem formed can be:

And the answer to the formed problem will be 26 miles.

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Answer:

f=4

Step-by-step explanation:

I think it's right but not 100% sure

[tex]x^{2} + 2x - 15 = 0[/tex] -> [tex](x+1)^{2} - 16 = 0[/tex]

-> [tex](x+1)^{2} = 16[/tex]
-> x+ 1 = 4 or -4
-> x = 3 or -5

Answer:

[tex]x=3, \quad x=-5[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+2x-15=0[/tex]

Step 1

Move the constant to the right side of the equation:

[tex]\implies x^2+2x-15+15=0+15[/tex]

[tex]\implies x^2+2x=15[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=15+\left(\dfrac{2}{2}\right)^2[/tex]

[tex]\implies x^2+2x+1=15+1[/tex]

[tex]\implies x^2+2x+1=16[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+1)^2=16[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+1)^2}=\sqrt{16}[/tex]

[tex]\implies x+1=\pm4[/tex]

Step 5

Subtract 1 from both sides:

[tex]\implies x+1-1=-1\pm4[/tex]

[tex]\implies x=-1\pm4[/tex]

Solutions

[tex]\implies x=-1+4=3[/tex]

[tex]\implies x=-1-4=-5[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=3, \quad x=-5[/tex]

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The 3 : 7 ratio of the leg lengths and the 42 cm length of the hypotenuse side using Pythagorean theorem, gives the lengths of the sides (the legs of the right triangle) as follows;

[tex]147 \cdot \sqrt{ \frac{2}{29} } [/tex] and [tex] 63 \cdot \sqrt{ \frac{2}{29} }[/tex]

Pythagorean theorem states the square that has the hypotenuse of a right triangle as its side length is equal in area to the sum of the areas of the two squares formed by legs of the right triangle.

Given;

The possible given parameters are;

The ratio of the length of the sides (the legs) of the triangle is 3 : 7

The length of the hypotenuse side = 42 cm

Required: The lengths of the other two sides of the triangle

Solution;

The lengths of the two sides are found as follows;

Let a and b represent the lengths of the legs of the right triangle, according to Pythagorean theorem, we have;

a² + b² = 42²

The ratio of the leg lengths gives;

a/b = 3/7

Therefore;

a = (3/7)•b

Which gives;

((3/7)•b)² + b² = 42²

b²•((3/7)² + 1) = 42²

b = 42²/(((3/7)² + 1)) = 42²×(58/49)

[tex]b = 147 \cdot \sqrt{ \frac{2}{29} } [/tex]

Which gives;

[tex]a =\frac{3}{7} \times 147 \cdot \sqrt{ \frac{2}{29} }= 63 \cdot \sqrt{ \frac{2}{29} }[/tex]

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When Jerry puts 1500 pounds in the bank for 5 years then the rate of interest which makes the amount equal for Jerry and Neil is 1.85%.

Given Neil puts 1550 pounds in the bank, at a rate of 3% compound interest.

we need to calculate the total amount and interest at the end of 5 years.

P=1500 pounds

r = 3%

n = 5 years.

A = P(1+r/100)ⁿ

A = 1500(1+3/100)⁵

A = 1500(103/100)⁵

A = 1500 × 103/100 × 103/100 × 103/100

A = 3278181/2000

A = 1639.09

C.I = A-P

= 1639.09 - 1500

= 139.09

From the question, After 5 years they have the same amount.

Therefore we use the amount to calculate rate of interest as :

A = 1639.09

Simple interest = 1639.09 - 1500

= 139.09

Therefore, P = 1500

I = 139.09

t = 5 yrs

R = (100×I)/(P×t)

R = (100×139.09)/(1500×5)

R = 1.85%

Hence the rate of interest is 1.85%.

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Question 1

[tex]2l+2w=48 \\ \\ 2l+20=48 \\ \\ 2l=28 \\ \\ l=14\text{ cm}[/tex]

Question 2

[tex]2l+7.2=48 \\ \\ 2l=40.8 \\ \\ l=20.4 \text{ cm}[/tex]

Question 3

[tex]2l+2w=48 \\ \\ l+w=24 \\ \\ w=24-l[/tex]

Answer:

Step-by-step explanation:

The equation that can be used to determine the number of onion rings and the number of chicken wings are x + y = 19 and 40x + 75y = 970.

To verify a proportionality, that is, whether the quantities are proportional or not, we must make an equality of ratios. If these ratios are equal, the values ​​will be proportional.

Let x represent the number of onion ring and y represent the number of chicken wings.A combination meal with onion rings and chicken wings has a total of 19, hence:

x + y = 19      (1)

Also, they altogether contained 970 calories:

40x + 75y = 970     (2)

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Considering the numeric values of the function, we have that:

a) S(0) represents the remaining number of socks after 0 pairs are sold, and S(6) represents the remaining number of socks after 6 pairs are sold.

b) S(0) = 14, S(6) = 12.

c) The domain is not all real numbers, as the remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

For this problem, the function is given as follows:

S(p) = 14 - 2p.

In which S(p) is the remaining number of socks after p socks are sold.

Then the numeric values are:

The domain of a function is the set that contains all possible input values of the function. The remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7, and the graph is given at the end of the answer.

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Answer:

D. The last 26/8, 3-32, -Pi, -4 2/3

Step-by-step explanation:

26/8= 3.25

3-32=3.17

-Pi= -3.14

-4 2/3= -4.67

When x is made the subject of m= n+ x/p,

          x = mp - n

How is  x  made the subject of m = n +x/p ?

[tex]m = \frac{n+x}{p} \\\\mp = n+x\\\\mp -n = x\\\\x = mp-n[/tex]

How is x being made the subject?

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Answer:

hello!

your answer would be 258, because the y-intercept goes upwards.

:D have a good day <3

Answer: no idea

Step-by-step explanation:

Using proportions, it is found that the scale of the rectangle is of 1:14.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division to find the unit rates.

One example of application of proportions is for scale problems, as the scale is given by the following equation:

Scale = Drawn distance : Actual distance.

For this problem, we have that:

Hence the scale is of:

6.1 : 85.4.

We can simplify dividing 85.4 by 6.1, hence:

85.4/6.1 = 14.

Hence the simplified scale is:

1:14.

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the scale of the drawing of the rectangle.

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The Graph of the Equation |x-1| +5 = 2 is attached below

This is further explained below.

Generally, An equation is a mathematical statement that demonstrates that two mathematical expressions have the same value.

This is the most basic version of the definition of an equation in algebra. For example, the phrase "3x + 5" = 14 is an equation, in which the two expressions "3x + 5" and "14" are separated by the symbol for "equal."

In conclusion, Please find attached the graph representing the equation "x-1 + 5 = 2."

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Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

Answer:

£32

Explanation:

so 1/5 = 0.2

to make 0.2 a percent just multiply by 100 so 0.2 • 100 = 20%

so the discount would be 20%, meaning the game holds 80% of its value since

100-20 = 80

so to make 80% a decimal, divide by 100 so 80/100 = 0.8

so then you just multiply: 40 • 0.8 = 32

so the game is £32

hope this helps :)

The price of the computer game on sale is  £32.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The normal price of a computer game is £40.

The price is reduced by 1/5 in a sale.

∴ The price of the computer game on discount can be obtained if we subtract the fraction of the discount times the normal price from the normal price which is,

= {(40 - (1/5)×40}.

= {40 - 8}.

= £32.

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Answers:

a)  2710 kg/m³

b)  5149 kg

====================================================

Work shown for part a)

density = mass/volume

density = (6775 kg)/(2.5 m³)

density = (6775/2.5) kg/m³

density = 2710 kg/m³

-----------------------------------

Work shown for part b)

density = mass/volume

mass = density * volume

mass = (2710 kg/m³) * (1.9 m³)

mass = (2710*1.9) kg

mass = 5149 kg

Thee surface area of the water tower is 1664 square feet

It is important to note that the formula for determining the surface area of a cylinder is expressed as;

Surface area = 2πr² + 2πrh

Where;

Also, note that the formula for diameter is expressed as;

Diameter = 2r

Substitute the value of diameter

30 = 2r

r = 15 feet

Now, substitute the values into the formula

Surface area = 2(3.14)(15)² + 2(3.14)(40)

expand the bracket

Surface area = 1413 + 251. 2

Add the values

Surface area = 1664. 2

Surface area = 1664 square feet

Hence, the value is 1664 square feet

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The smallest possible range of the chosen integers is; 2015

First of all, the range of a set of numbers is the difference between the largest and smallest numbers in the set.

The smallest range of a set of four different positive integers is 3. This occurs when the integers are consecutive, and only in this case. We first show that we cannot have four consecutive integers

with a mean of 2017.

Assume, to the contrary, that n is a positive integer such that the consecutive integers n, n + 1, n + 2 and n + 3 have 2017 as their mean.

Thus;

[n + n + 1 + n + 2 + n + 3]/4 = 2017

4n + 6 = 2017 * 4

n = 2015.5

Since n is an integer, then this can't be true. However, with a little tweaking of this, we can tell that we can use 2015 as our least integer.

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The definition based on the given biconditional is B. A polygon is a hexagon with six sides.

A conditional statement combined with its opposite is known as a biconditional statement. As a result, one conditional is only true if and when the other is also true. It frequently employs the phrase "if and only if" or the abbreviation "if." It serves as a reminder that the conditional must be true in both directions by using the double arrow.

The biconditional statement is that the polygon is a hexagon if and only if it has six sides.

Therefore, the correct option that illustrates this is B.

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The most appropriate choice of percentage will be given by-

£47 after 24% decrease becomes £35.72

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Original Price = £47

Percentage decrease = 24 %

Decrease in Price = £([tex]\frac{24}{100} \times 47\\[/tex])

                              = £11.28

New Price = £(47 - 11.28)

                 = £35.72

So, £47 after 24% decrease becomes £35.72

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Answer:

21

Step-by-step explanation:

If it loses 3 gallons every mile, then multiply it by 7.

3*7 = 21

Another way to solve this is by using linear equations

y=3x

replace x with 7 and y would be equal to 21

Answer:

Yes, the friend is correct.

Step-by-step explanation:

Twice a number of x is the same as saying multiply x by 2, which equals 2x. At most means 2x can only reach -24 at the very max, so solving for x will give you an answer that should only either be less than or equal to -24. This equation is an inequality because an inequality compares two values; in this case, the inequality is comparing 2x is at most -24, which is the same as saying 2x is less than or equal to -24.

Answer:

350%

Step-by-step explanation:

1) To convert a decimal to a percentage multiply the given decimal by 100. So,

3.5 x 100 = 350

2) 350% is the final answer

A: To make it more pumpkin-y, Pumpkin Puree or Pumpkin Spice. To make it less pumpkin-y, Banana, milk, or yogurt.

Answer:

25 mph

Hope this helps! :)